Conventional quantum cascade lasers (QCLs) have used square (symmetric when not under an applied bias) quantum wells. At least in part because conventional QCLs use square quantum wells, it is not possible in conventional QCLs to place both the radiative and LO-phonon transitions within one single quantum well when the radiative transition energy spacing is smaller than the LO-phonon energy spacing (as can be for terahertz QCLs).
The first QCL was a mid infrared laser that used LO-phonon scattering for depopulation; however, the diagonal transitions that were used for both the phonon and radiative transitions are generally not well suited for terahertz applications (J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, Science, 264:553 (1994)).
Other conventional square four quantum well and three quantum well LO-phonon terahertz QCLs have been developed. They use at least two quantum wells for the radiative transition and a third quantum well which uses two energy levels; one energy level is used to resonantly tunnel the lower lasing state and the other arranges the lower state, approximately spaced at the LO-phonon energy. While these configurations can have vertical transitions, they use more than one quantum well for the radiative transition, and due to the use of resonant tunneling of the lower lasing state, the lower lasing state always has a doublet of states (for example, see quantum states E4 and E3 in FIG. 5 of U.S. Pat. No. 7,158,545 to Qing Hu, et al.). This doublet of states can provide a mechanism of absorption loss of terahertz radiation in the lower frequency of operation limit. (Q. Hu and B. S. Williams, “Terahertz Lasers and Amplifiers Based on Resonant Optical Phonon Scattering to Achieve Population Inversion,” U.S. Pat. No. 7,158,545, Filed Sep. 12, 2003, issued Jan. 2, 2007) (H. Lou, S. R. Laframboise, Z. R. Wasilewski, G. C. Aers, and H. C. Liu, Appl. Phys. Lett, 90, 04112 (2007)). Also, oscillator strengths typically range from ˜0.5 to less than 1.
Conventional LO-phonon QCL configurations can experience unwanted parasitic injection into the lower lasing state. Attempts to reduce that unwanted parasitic injection have been made by adding an additional well at the injector, but the oscillator strength was reduced with this type of approach (S. Kumar, B. S. Williams, J. L. Reno, Appl. Phys. Lett. 88:121123 (2006)).
Miniband approaches, such as the bound to continuum approach that features minibands and a somewhat isolated radiative state (G. Scalari, L. Ajili, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies, Appl. Phys. Lett. 82:3165 (2003)) as well as hybrid miniband configurations with optical-phonon scattering (G. Scalari, N. Hoyler, M. Giovannini, and J. Faist, Appl. Phys. Lett. 86:181101 (2005)), have also been pursued. Oscillator strengths for miniband configurations are sometimes listed higher than their LO-phonon configuration counterparts; however, this is somewhat offset since their section lengths are about twice as long as compared to LO-phonon configurations. Miniband configurations can also be more susceptible to thermal back filling.
The importance of improving the injector efficiency can be seen by the following approximate 2D population inversion relation:
      Δ    ⁢                  ⁢          n              2        ⁢        D              =            η      ⁢              J        e            ⁢                        τ          2                ⁡                  (                      1            -                                          τ                1                                            τ                21                                              )                      -                  (                  1          -          η                )            ⁢              J        e            ⁢              τ        1            where η is the injection efficiency, e=1.602 176 53(14)×10−19 Coul., J is the current density, Δn2D is the 2D population inversion, and the state lifetimes are represented by τ. The population inversion can be improved by increasing the injection efficiency, having a long upper state lifetime, and by having τ1<<τ21.
It is to be understood that the foregoing and the following description are exemplary and explanatory only and are not to be viewed as being restrictive of the invention, as claimed.